The life of Enrico Fermi: phase two
In the summer of 1926 Fermi, at this point well introduced into the Roman group of famous scientists and intellectuals, met and wooed a student of Natural Sciences, Laura Capon, his future wife and first biographer.
“Corbino’s boys worked together in a natural and spontaneous way. The teaching of physics was done without formality, low-key. Pupils and students put their forces together to solve the toughest problems under Enrico Fermi’s direction. Fermi would show up with his problems and would think out loud with the help of chalk and blackboard in front of the others. This way they learned how to use logic to confront physics problems.
As a reminder of those relaxed, unceremonious get-togethers there is still the old table in Fermi’s room around which maestro and students would sit. There’s a big hole in the middle where an angry Emilio Segrè slammed his fist one time when the others wouldn’t let him speak when he wanted to. He got annoyed easily and for this was nicknamed Basilisk.”
Among Fermi’s various teachings the new theory of quantum mechanics was at the center of the discussions because, even though difficult and non-intuitive, it was the novelty of international research.
“Quantum theory is a dogma, not a fact that can be demonstrated by reason, the students used to say. It’s a question of faith. In questions of faith the Pope is infallible. In quantum theory, Fermi is infallible therefore Fermi is the Pope. Rasetti, who would take Fermi’s place in his absence was nominated Cardinal Vicar. Majorana with his hypercritical acumen who would bring attention to the slightest contradiction and tiniest error was called the Grand Inquisitor.”
Enrico Persico arrived in Rome from Torino for a brief visit but brought bad news: the number of adepts to quantum theory was extremely limited and the number disagreeing with it extremely large.
“The Pope was profoundly disturbed by the news and immediately nominated Persico as “Propaganda Cardinal of the Faith” with the job of preaching the Good Word to the infidels. Edoardo Amaldi was the “Abbott”, being the youngest of the group. When the young Bruno Pontecorvo joined the group at Via Panisperna in 1933, he, too, chose a nickname just right for his condition: “the Puppy.”
After his formidable success in theoretical fields like quantum statistics that carry his name, and the beta ray theory that introduced a new type of fundamental force, the weak interaction, Fermi moved his research in 1929 in the experimental realm towards nuclear physics. This new line of inquiry would be the theme of an international physics conference in Rome precisely at the Institute at Via Panisperna in October of 1931. Fermi was one of its stars.
In 1934 the possibility of producing artificial radioactive elements by bombarding different elements with charged particles became a reality thanks to Irene Curie and Frédéric Juliot. Fermi and his boys threw themselves into this new pursuit using some newly discovered particles—neutrons—that had the advantage of not being affected by the electrostatic repulsion of the nucleus.
“Enrico begins to search for a neutron source and finds it thanks to the intervention of “Divine Providence” in the person of Professor Giulio Cesare Trabacchi that had been saving a gram of Radium in the underground bowels of the Physics Institute.”
Wanting to bombard the elements in order of the periodic table in a systematic way, Fermi brought in two new young graduates, the chemist Oscar D’Agostino and physicist Bruno Pontecorvo. The results, culminating in the comprehension of the fundmental role of slow neutrons in nuclear reactions, was sensational. In practical and technological terms they opened the way to applications of nuclear energy in only a few years: after only 40 years the consequences of Einstein’s theory became reality and Enrico Fermi became the father of the atomic age. These scientific results would win him the Nobel prize in 1938.
Fermions and Bosons
Fermi Dirac statistics
At the beginning of the Twenties of the last century it became evident that atoms and molecules with an even number of electrons are chemically more stable than those with odd numbers of electrons. It was thought that groups of electrons occupied a series of “electronic shells“ around the nucleus. Niels Bohr updated his atomic model assuming that the orbits of a certain number of electrons corresponded to stable shells. The orbits of an atom are characterized by a series of values of physical size that correspond to specific numerical values for energy, rotational speed and distance from the center. These numbers are called quantums. How are these numbers determined? And why do some of them correspond to stable shells?
Austrian physicist Wolfgang Pauli looked for a theoretical explanation for these numbers that had been found empirically. Pauli was convinced that the number of electrons in close shells can be understood if the electron’s orbit is identified by another quantum number besides those three already known. The new number was identified as “spin“ that, in certain units, can have integer or half-integer values. Spin describes a physical aspect that resembles the rotation of a particle on its own axis.
Pauli also theorized that, in every atomic system, no electron could share the same group of four quantum numbers with another electron because in this way the series of observed numbers was perfectly explained. The implications of this hypothesis are surprising: two electrons can be in the same place at the same time in an orbit with the same frequency and orientation as long as the fourth quantum number is different. This is Pauli’s “exclusion principle“ that today is one of the fundamental principles of quantum mechanics and which affirms that two identical particles with semi-integer spin, such as electrons, cannot share the same set of quantum numbers. In other words, they cannot occupy the same quantum state at the same time. It was shown that Pauli’s exclusion principle is responsible for the stability of ordinary matter and is evidence that it occupies volume. This was suggested for the first time in 1931 by Paul Ehrenfest, who stressed that the electrons in every atom can’t all fall into lower-energy orbits and must occupy gradually larger shells. Atoms thus occupy volume and can’t be squashed too tightly together.
Fermi learned to manipulate Pauli’s exclusion principle and began to reflect on how to extend this principle from electrons orbiting around an atomic nucleus to single atoms in a gas: if the electrons, instead of orbiting around the nucleus, were diffused throughout a finite volume, how would they act? Responding to this question, Fermi was able to explain the strange behavior of certain gases that under high pressure or low temperatures exhibited a strange drop in thermal capacity. The difference between classical statistical mechanics and Fermi’s new interpretation is essentially the following: in the classical version, the absence of heat implies the absence of movement and all atoms are found to be in a lower energy state. In Fermi’s version, however, certain atoms will end up in higher energy states because even in the absence of heat, according to the Principle of Exclusion, it’s impossible for two atoms to be in the same state thus having the same energy.
Fermi’s article immediately made a great impact because, applying Fermi’s statistics, various physicists were able to calculate the behavior of electrons in metals, obtaining predictions that coincided with experimental data. The article’s fame reached England and was read by Paul Dirac. But Dirac soon forgot about it since the problem didn’t interest him at that moment. A few months later, however, he began taking an interest in it and, starting from scratch, he came up with a slightly different method that came to the same analytical conclusions as Fermi. Fermi wrote to Dirac to claim his priority in the discovery which Dirac acknowledged and so from that moment on it has always been referred to as the Fermi-Dirac statistics, generously attributing the major part of the discovery to Fermi. If we now call “fermions“ those particles that obey the principle of exclusion it’s precisely because Dirac acknowledged Fermi’s precedence in the discovery.
The Fermi-Dirac statistics describe the behavior of particles that have a semi-integer spin value and is widely used to study electrons in solids; it’s also the basis of electronics and semiconductor physics which made possible discoveries like the transistor.
Particles with integer spin, like photons, follow the Bose-Einstein statistics and are called “bosons“ in honor of the Indian physicist Satyendra Nath Bose who first theorized them, sending his results to Albert Einstein who comprehended their importance and had them published. Bosons, not following Pauli’s exclusion principle, can occupy in unlimited numbers, the same energetic state simultaneously and, at low temperatures tend to accumulate at the same low-energy level, forming a Bose-Einstein condensate. The Bose-Einstein statistics are particularly useful in the study of gases.